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By Baruch Grinbaum, Edwin Bwalya, Robert Minango, Deogratias Bukunkwe

Solvent extraction of Cu from acidic leach, using an oxime extractant, e.g. LIX 984 or Acorga is a well known and established process. As the process advances, Cu is extracted to the solvent and is replaced by H+ in the aqueous phase. At high acidity the distribution coefficient of Cu between the solvent and the aqueous phase decreases, and eventually relatively high concentration of Cu remains in the raffinate, regardless of the number of equilibrium stages. In many processes this phenomenon is immaterial, as the raffinate returns to the leaching and no copper is lost. But when the copper raffinate is used for processing of additional metals, minimal concentration of Cu in the raffinate is essential for an effective process. The recommended process includes three steps: 1. SX-1: Standard extraction of Cu with oxime. The resulting raffinate contains about 6-8 g/L Cu and 50 g/L H2SO4. 2. SX-N: Extraction of most of the acid into an amine-based solvent, and stripping it with a base, e.g. aqueous ammonia, caustic, Na2CO3 etc. The extraction removes no metals, but decreases the concentration of acid from 50 to 10 g/L. 3. SX-2: Extraction of the neutralized solution once more with oxime, to remove the residual copper. Such a process enables one to get down to 100-150 ppm Cu in the final raffinate. This process was developed and tested in the R&D facility in Chambishi Metals plc, by a joint team of Chambishi & Bateman, using Cognis LIX 984N and real solutions from the plant. In the laboratory scale, the equilibrium isotherms for SX-1, SX-2 and the neutralization were developed. Computer simulation of the results showed that the optimal configuration is two stages for both extraction and stripping for SX-1. For SX-2 2-3 stages of extraction and two stages of stripping are needed. The stripping stages may be common to both SX-1 and SX-2. The neutralization of SX1 raffinate was tested both by conventional precipitation with lime and by extraction with Alamine based solvent extraction and stripping with a solution of 10% NaOH. For the SX-N only one stage was needed for both the extraction and stripping. The bench scale pilot plant was run for both SX-1 & SX-2. The results were very similar to the simulated ones, and the configuration of 2E2S for SX-1 and 3E=2S for SX-2 delivered the required raffinate with less than 150 ppm Cu.

Jan 1, 2005

By G. Tranell, L. Kolbeinsen, S. Gaal, J. Safarian

The effect of carbon material properties on the rate of MnO reduction from ferromanganese slag by solid graphite was investigated. A sessile drop technique was used to study the reduction rate of a synthetic slag containing 45 wt% MnO at 1500 and 1600 ºC. Different types of graphite substrates were used and the con-tact angle between slag droplets and substrate were measured in-situ. Moreover, the slag droplet volume during the interaction with the graphite substrates was calculated and normalised. The mathematical relationship between the slag density during the reduction and the normalised slag droplet volumes during the reduction were derived and the MnO reduction curves were then calculated. A method for measuring the slag reactivity of solid carbon was defined and used to qualify the propensity of the different graphites to react with the liquid slag. Some supplementary studies such as manganese evaporation measurement and EPMA analysis for determining the extent of MnO reduction were also carried out. It was observed that there is nota significant difference in the wetting angle of the graphite substrates by the slag, and the wetting is not changed within the temperature range of 1500-1600ºC. However, the changes in the contact angle during the slag reduction at 1600ºC are more than at 1500ºC. The kinetics of MnO reduction is dependent on the type of graphite and it is more dependent on the graphite properties at lower temperatures. On the other hand, the dominant properties of graphite on the reduction rate vary with temperature. A multivariate analysis on the graphite properties and the parameters related to the slag reactivity indicated that the kinetics of MnO reduction is mainly dependent on the temperature, and then on the graphite properties. It was also found that at1500 ºC the surface area and the CO2 reactivity are the most important graphite properties for the slag reduction, suggesting that the reactivity of carbon is rate controlling at 1500 ºC. However, the porosity related parameters are the most important graphite properties at 1600 ºC, suggesting that CO gas desorption is rate controlling at high temperatures.

Jan 1, 2007

By Godofredo F. Barrios

For years urethane screen surfaces have been used in a wide range of wet screening applications where openings from as fine as 100 microns and coarser have been used. The purpose of this paper is to expose the reader to new developments in both screen surface and screening equipment technologies which allow an end user to consider urethane screen surfaces for fine screening applications. These technologies allow an end user to use the inherent advantages of urethane with regards to wear resistance while also realizing the benefits that a high oper area urethane screen surface can bring. These benefits include non blinding characteristics and feed capacities that which rival that of traditional stainless steel surfaces. The paper will highlight the features of this patented urethane screen surface technology and the screening machines they are used in conjunction with. There will also be a presentation of case studies of commercial installations where these technologies are utilized. These case studies are from the base metals industry therefore relevance to the conference is direct and not inferred. Included in the paper will also be constraints which must be taken into account when considering urethane screen surfaces such as temperature and chemical attacks. This paper will expose potential end users to a possibility of using screens to achieve extremely accurate size separations in applications where screens were previously not considered. The paper will explain and demonstrate that prior concerns of screen surface blinding, high screen surface consumption rates and large screen surface area requirements can be eliminated by proper utilization of high open area urethane screen surfaces.

Jan 1, 2007

Many industries base their decisions on the assaying of tiny analytical sub-samples. The problem is that most of the time several sampling and sub-sampling stages are required before the laboratory provides its ultimate assays using advanced chemical and physical methods of analysis. As long as each sampling and sub-sampling stage is the object of due diligence using the theory of sampling it is likely that the integrity of the sought after information has not been altered and the generated database is still capable to fulfil its informative mission. Unfortunately, more often than not, unawareness of the basic properties of heterogeneous materials combined with the unawareness of stringent requirements listed in the theory of sampling, lead to the conclusion that massive discrepancies may be observed between the expensive outcome of along chain of sampling and analytical custody, and reality. There are no areas that are more vulnerable to such misfortune than sampling and assaying for trace amounts of constituents of interest in the environment, in high purity materials, in precious metals exploration, food chain, chemicals, and pharmaceutical products. Without the preventive suggestions of the theory of sampling serious difficulties may arise when making Gaussian approximations or even lognormal manipulations in the subsequent interpretations. A complementary understanding of Poisson processes injected in the theory of sampling may greatly help the practitioner understand structural sampling problems and prevent unfortunate mistakes from being repeated over and over until a crisis is reached. This paper presents an overview of the theoretical, practical and economic difficulties often vastly underestimated in the search for quantifying trace amounts of valuable or unwelcome components.

Jan 1, 2010

The EMEM Awards of the Department of Minerals and Energy (DME) were formally launched on 3 March 2000 by Ms Susan Shabangu, Deputy Minister at the Department?s Mineralia Centre in Pretoria. The launch was attended by invited guests from the mining and aggregate industries ,representatives of the Patron Organisations (see below),non- government and scientific organizations, the media, other government departments involved with mining environmental management and members of staff of the DME both nationally and regionally.

Jan 1, 2000

By P. Valicek

Anglo American Platinum Limited is constantly striving to improve safety and productivity. There are many different initiatives taking place within the organization in order to ensure continued safe operation and profitable ounces for the future. One of the opportunities and potential growth areas that has been identified and is being explored is that of mechanization. In order to do this, the approach that has been adopted by Anglo American Platinum is to fully understand and analyse the current mechanized mining methods. Once each configuration is fully understood, the method can then be optimized and new mining technologies and systems can be developed to overcome the current shortfalls. This paper will discuss a methodology that was developed by Anglo American Platinum (in conjunction with Cyest Corporation) and adopted to optimize the mechanized mining layout and fleet configuration, and will also present the final findings of the study. Due to the impracticability of piloting every possible option in the workplace, extensive modelling and simulation exercises were conducted to determine realistic parameters for productivity and value. The study resulted in a full understanding of mechanized mining systems and their associated layout. From the results of the study a mining / logistic layout was developed which highlighted the following opportunities: 1. Create safe operations through the reduction of personnel in the ?high-risk zone? of stopes 2. Separate machines and personnel by use of remotely operated machines 3. Create focused mining on primary development from the production stoping, thus having dedicated teams on development and stoping. 4. Develop primary development ahead of the stoping activity. This enables: a) Understanding of the geology and subsequent implementation of the correct b) technology (?fit-for-purpose?) required to mine that area based upon this geological knowledge c) Ability to install tipping points ahead of stoping, creating ?immediate stoping reserves?, thus increasing flexibility and reducing production risk d) Improved productivity by having adequate faces available and reduction in re-development to establish faces. 5. Quicker return on Investment due to recovering revenue from ?on-reef development? 6. The layout allows flexibility between stope sections enabling better ?resource sharing? 7. Optimize the long-term ratio of machine makeup of the fleet in relation to the production outputs 8. Creates an agile mining layout allowing rapid response to market pressures. The findings and work presented in this paper is currently being implemented at different test sites within Anglo American Platinum and will demonstrate that improved safety and productivity can be achieved through the adoption of mechanization.

Jan 1, 2012

By S. Pal, A. K. Lahiri

Most of the compounds present in slag are surface active. This gives rise to foaminess of slag. The foam life and foaming index are normally determined by the draining rate of slag through the plateau border, so the foaming index is directly proportional to slag viscosity and inversely proportional to slag density and bubble diameter. When a small amount of a strong surface active compound like P2O5or Cr2O3is present in slag, however, the foam life increases significantly and the above relationship is not obeyed. The strong surface active compounds reduce the draining rate from the film between the adjacent bubbles so the film draining controls the life of the foam. The thickness of the film, Marangoni force, viscosity of the slag, and diffusion of surface active compounds determine the film draining rate. The interplay of these factors leads to very low or high film draining rates and affects the film and foam stability significantly. Keywords: slag, foam, foaming index, film draining

Jan 1, 2004

By B. L. Eggers

This study investigates the application of computed order tracking with subsequent rotation domain averaging and statistical analysis, to the drag gearbox of a dragline used in a mining environment. Computed order tracking is a fault detection method developed to deal with the varying speed conditions often found in industry and has been proven effective in laboratory conditions. Its application to real situations, however, requires some adjustment to deal with issues such as inadequate speed data and the fact that the drag gear rotates in two directions. This provides a unique opportunity to observe the performance of the order tracking method in a bi-directional rotating environment, allowing an investigation of the relationships between the results obtained from each operating direction. A monitoring station was set up aboard the dragline and data was captured twice daily for a period spanning approximately one year. The data captured consisted of accelerometer and proximity sensor data. The key on the shaft triggers the proximity sensors, allowing speed and direction to be measured. The measured speed is interpolated by using various speed interpolation techniques. Then the interpolated speed is used to complete the order tracking procedure that resamples the vibration data with reference to the speed. The results indicate that computed order tracking can be successfully employed in real environments. Furthermore it is shown that the rotation direction that opens the gear-tooth crack gives a better indication of incipient failure. It is therefore important not to disregard either direction when monitoring rotating machinery of this kind.

Jan 1, 2007

By C. Birch

"A mineral resource royalty is payment to the holder of mineral rights for the utilization of the mineral resource. In South Africa, this payment is made to the State as holder of the mineral rights (The Mineral and Petroleum Resources Royalty Act of 2008). The principle purpose of this research paper is to identify if the State is benefitting from the mineral resource royalty by considering its impact on seven individual Witwatersrand gold mines.For this study, a simple financial optimiser model was created in Microsoft Excel that links the ore flow, block listing and the cash flow (excluding or including the cost of the mineral resource royalty). Mixed integer linear programing (the Excel Solver function) is utilised to optimise either profit or NPV (at 9% and 12%) by adjusting the cut-off grade.The impact on each of the seven mines mine was different but overall R7.9 billion is estimated to be paid in mineral resource royalty over their expected remaining lives. Due to the cost of the mineral resource royalty and increasing the cut-off grades, the total revenue decreases by R10 billion. A significant portion of this lost revenue would have been paid to the State in the forms of other taxation including company income tax which decreases by R2.8 billion. It is recommended that an industry wide investigation be conducted to determine if the resource royalty is adding to the State’s revenue, or destroying value including premature job losses. IntroductionTaxation of mining companies has become a very topical subject in the context of the postapartheid South African economy. There have been increasing calls for equitable re-distribution of mineral asset wealth for the benefit of all South African citizens and not just to an elite few. As part of the Mineral and Petroleum Resources Development Act (MRDPA) of 2002, the Mineral and Petroleum Resources Royalty Act of 2008 was introduced and came into effect in 2010 (South African Revenue Services, 2008). A mineral royalty is payment to the holder of mineral rights for the utilization of the mineral resource. In the case where the holder of the mineral right is the State, then this payment is made to the State (Cawood, 1999). Studies on the potential impact of the mineral resource royalty on the minerals industry have been conducted during the formulation of the Act and subesquently. These include Cawood and Macfarlane (2003), who suggested a cap of no more than 3% (Cawood and Macfarlane, 2003), as well as Cawood (2011), who predicted rising cut-off grades and thus reducing mineral reserves. In 2013, Grobler completed a Masters in the Faculty of Economic and Management Sciences at the University of Pretoria and concluded that the impact of the mineral resource royalty on the economy is positive. She stated that the royalty has caused operating expenses to increase, but this does not appear to be significant. Furthermore, she stated that the royalty has not affected the way the mining industry operates (Grobler, 2014)."

Jan 1, 2016

By A. Z. Toper

This is a sampling of the papers presented at the conference, the proceedings can be bought from the SAIMM An extensive research programme to address the issue of rockburst control has been undertaken over a number of years. This paper discusses the development of preconditioning techniques to control face bursts, for safer mining in seismically hazardous areas. Preconditioning involves regularly setting off carefully tailored blasts in the fractured rock immediately ahead of a mining face, so as to encourage slip on pre-existing fractures, in order not to allow the accumulation of high strain energy density in the rock mass. Two different preconditioning techniques have been developed, namely face-perpendicular preconditioning and face-parallel preconditioning. Both have prevented face bursting in areas to which they have been applied, even though several large seismic events have occurred close to the faces in some areas. In addition, minimal overall damage was observed in the preconditioned panels following these events, compared to similarly exposed unpreconditioned panels. Preconditioning has also provided some protection to the face area from distant events, through the capacity of the preconditioned ground to absorb energy. An improvement in hangingwall stability and productivity has also been noted in preconditioned areas. In order to determine the optimum blast parameters for achieving the most effective preconditioning, an extensive optimization study was carried out for the face-perpendicular preconditioning technique. While optimum values for parameters such as hole length, diameter and spacing were determined, it was ultimately concluded that the differences in results obtained by varying the preconditioning parameters were less significant than the clear positive differences observed when comparing preconditioned areas with non-preconditioned areas.

Jan 1, 2000

By R. G. Cawthorn

The earliest authenticated scientific report of the occurrence of platinum in rocks from the Bushveld Complex appears to be by William Bettel on 10 November 1906. Thereafter, prospecting of the chromite-rich rocks for platinum proved frustrating. I suggest that the resurgence of interest shown by Dr Hans Merensky in 1924 resulted from his realization that newly panned platinum had a different grain size from that in the chromite layers and indicated a different source rock, which he located, and it became known as the Merensky Reef.

Jan 1, 2007

By N. Sahay

Improvement in work place environment by conventional methods viz., installation of higher capacity fan, fans in parallel operation or booster fan is a risky proposition in many coal mines in India because of difficult geo-mining condition such as shallow depth, multi seam workings having thin parting and inter connected goaves one above the other. The situation is further worsened if the mines have fire affected sealed off area connected to different ventilation circuits. On many occasions circulation of more air quantity by increasing fan pressure have resulted in initiation of spontaneous heating. To address these problems, authors have made some improvement in conventional Dynamic Balancing of Pressure Technique and worked out few ventilation schemes which are aimed for neutralization of pressure differential across sealed off area at the same time having improvement in ventilation in the mine. The excess pressure differential across sealed off area is mainly caused by introduction of higher capacity fan. Similar situation prevailed in one of the mines of Jharia Coalfield, India. The problem was solved by application of the above technique. In this paper, brief description of the technique, the problem in the mine, results of investigation, computer simulation studies of various schemes and methodology adopted for implementation of the technique in the mine have been discussed in some detail. Keywords: Dynamic Balancing of Pressure Technique, Spontaneous heating, Work place environment.

Jan 1, 2003

By N. A. Smith, R. J. Fowell, J. L. Hislam

Abstract: Data are presented from two sites in southeast England, where problems were encountered in tunnelling through ground containing flint. In response to the difficulties, substantial laboratory testing programmes were initiated to determine the strength of the flints.It is shown that the strength varies very considerably, even within a single flint particle and that the practice of estimating unconfined compressive strength by a single multiplier applied to the point load strength index (Is(50)) may give misleading results. The preparation of UCS specimens for testing was found to be very difficult and it is recommended that tunnel machine capacity is assessed relative to Is(50). Résumé: Des données sont presentées sur deux sites dans le sud-ouest de l’Angleterre,où le perçage d’un tunnel dans un sol contenant du silex a posé des problémes. En consequences de ces difficultés, des programmes substatiels de recherché en laboratoire ont été initiés afin de déterminer la resistance des silex. Il est demontré que la resistance varie considérablement, même au sein d’une particule de silex, et que la pratique de estimation de la résistance en compression non confinée, (UCS) par le biais d’un simple coefficient appliqué au ‘point load strength index (Is50)’ pourrait donner des resultants trompeurs. La préparation de specimens UCS destinés aux tests s’est avérée trés difficile et il est recommandé que la capacité de la machine de perçage de tunnels soit calculée relativement au Is50. Zusammenfassung: Daten von zwei Standorten in Südosten von England, wo Probleme beim Tunnelbau durch feuersteinhaltigen Grund antraffen, sind angegeben. Wegen diesen Schwierigkeiten wurden Laboratoriumsforschungsprogramme eingeleitet, um die Festigkeit von Feuersteinen zu bestimmen. Es wurde gefunden, dass die Festigkeit sehr unterschiedlich war, selbst bei einzelnen Feuersteinstücken, und dass die Praxis, die unbegrenzte Kompressionsfestigkeit (uKf) auf Grund eines einzigen Multiplikationsfaktors vom Punktladefestigkeitsindex (Is50) abzuschätzen, zu irreführenden Resultaten führt. Die Vorbereitung der uKf Prüfstücke war sehr schwierig und es wird vorgeschlagen, dass die Kapazität der Tunnelbaumaschine in Abhang der Is50 bestimmt wird.

Jan 1, 2003

By E. Swart

The purpose of this paper is to provide an overview of the current legislative framework for mine closure within South Africa as well as the new requirements in terms of the Mineral and Petroleum Resources Development Act, 2002. The roles and responsibilities of Government, the mining industry and other stakeholders and confusion caused are also highlighted.

Jan 1, 2003

By S. Mundike

A scraper-based block cave method has been successfully applied to extract the Lower orebody at Nchanga since the 1950s. Since inception, scraper drifts and service ways have been supported using steel arch sets fabricated to a specific design from high strength manganese steel To reduce costs and to improve productivity, trials commenced in 2002 using fibre reinforced shotcrete as an alternative support method. One of the areas, the 2420 8E 1C trial drift, was subjected to abutment loading for several months prior to undercutting and cave mining. Shotcrete installed exhibited minor cracking shortly after application but very little deterioration thereafter. Following the success of the trial, the application of fibre-reinforced shotcrete was extended to other drifts. This paper describes the application of fibre-reinforced shotcreteat Nchanga and outlines design and quality assurance methods employed.

Jan 1, 2005

By P. Henning

Rock fall accidents continue to be the main cause of fatal and serious injuries in the mining industry. Although there has been an improvement in the FOG (falls of ground) related fatal and serious injuries over the past few years, the rate is still too high. New technology has made it possible to reduce this rate significantly. FOG accidents imply failure of the support system or the design of the support system in use. In this paper we deal with the latest technology available to assist the mines to reduce the rates of FOG related injuries and fatalities.

Jan 1, 2010

By H. Cevizci

"Numerical simulation of the plaster stemming method (PSM) was performed and compared with the conventional drill cuttings stemming method (DCSM). Many earlier in situ tests have proved that PSM can use the blast energy more efficiently than DCSM. Despite PSM generating more blast vibrations, it has advantages over DCSM such as better fragmentation and lower cost per unit volume of rock blasted. In this study, numerical simulation with Autodyn software using a 2D tool was employed to prove the efficiency of plaster stemming by comparing parameters such as pressure, Y-velocity, Y-force, internal energy, acceleration-Y, and compression. For example, the maximum pressure attained at the top of explosive column was 7 395 MPa for DCSM whereas it was as high as 11 945 MPa for PSM. Most of the computed parameters were significantly higher in PSM than those obtained for DCSM. This paper is the first study elucidating the efficiency of PSM by numerical simulation. It is concluded that PSM can save substantial amounts of money and effort. IntroductionThe stemming of blast-hole collars in surface mines with an inert material redirects blasting energy to the rock more efficiently, thus the blast-induced energy is utilized more effectively in breaking rock. With proper stemming, the gases should not escape due to loose stemming material. More efficient stemming with better confinement therefore increases the blast fragmentation. In addition, the distance of scatter is increased, giving rise to a looser rock pile that can be more easily loaded and transported. In order to improve the performance of a blast, stemming is used to help maintain the gas pressure over time (Konya and Konya, 2018). Proper stemming has been shown to increase the explosive efficiency by over 41% (Snelling and Hall, 1912).The most common stemming material in open pits and quarries is drill cuttings because of their ready availability at blast sites and the drill cuttings stemming method (DCSM) is a low-cost method. However, it has a major disadvantage in that dry drill cuttings eject very easily from blast-holes during an explosion, thus a great percentage of the blast energy is wasted and lost to the atmosphere. Cevizci (2012, 2014, 2013, 2017) studied blasting parameters in open pits and obtained better results with the plaster stemming method (PSM) in many limestone, basalt, and clay quarries. Moulding plaster is preferred for stemming because of the fast hardening time of 25–30 minutes."

May 1, 2019

By M. -O. Suk, S. -K. Jo, S. -C. Shim, J. T. Kim, S. -H. Kim, C. -W. Seo, J. -S. Kim

An equilibrium study was carried out at 1873 K to ascertain the effect of carbon in CaO-SiO2-Al2O3-MgO-MnO-FetO slag systems on their FetO and MnO activity coefficients, representing the slag?s thermodynamic potential for steel reoxidation. Both ?FetOand ?MnO showed not only a sharp increment, but also a simultaneous slow decrement by increasing carbon content in slag, suggesting opposite roles of the carbon according to its stable forms. XPS (X-ray photoelectron spectroscopy) was introduced to clarify the stable forms of carbon in slag. XPS results prove that carbon dissolves in slag as carbonate, and carbide ions under oxidizing and reducing atmospheres, respectively. It was concluded that carbonate ions increase ?FetOand ?MnO, and that carbide decreases them. This paper suggests an application method of the present results to actual ladle refining processes, in order to enhance steel cleanliness without decreasing (FetO + MnO) content in slag. Keywords: carbon, slag, activity coefficient, FetO, MnO, carbonate, carbide, XPS, reoxidation, cleanliness

Jan 1, 2004

By B. McCosker

The choice of the appropriate delivery process for a project is often not adequately thought about. The industry needs to be prepared to break its preconceived mind-sets on delivery procedures. Industry should also be prepared, on a project by project basis, to commit to a critical review as to how the assessment and then selection of the best procurement method can best optimize the project outcome for both client and contractor. Conventional standards and biased reliances and experienced based preferences should be challenged. To achieve this requires a paradigm shift in attitude to both the process of tendering and the evaluation of tenders. Tender and contracting practices are dynamic and have moved away from solely cost based assessments. Tendering contracts arise imposing changed duties upon owners. Traditional contract delivery models have shifted, reflected in part by the trend towards relationship contracting. The categories of contract options are not closed. Many are but hybrids of other time-tested models. This paper considers options available for any brownfield or greenfield project. The principles outlined are translatable to supply, upgrade, operation and maintenance arrangements.

Jan 1, 2002

A large number of brittleness concepts have been used in very different studies in the literature. One of them is the B1brittleness concept. In this study, the objective is to criticize the B1 brittleness concept on rotary blast hole drills. The B1 brittleness concept, the ratio of uniaxial compressive strength (sc) to tensile strength (sT), are widely used as a rock brittleness concept in the literature (Inyangand Pitt, 1990; Verhoef, P.N.W. 1993; Neil, D.M. et al.1994;Becker, et al.1984; Evans and Pomeroy, 1966; Göktan, R.M.1992; Kahraman, S. 2001; Yamaguchi, U. 1970; Verhoef, P.N.W. et al.1996; Bilgin, 1982; Howarth and Rowlands,1987; Howarth, D.F. et al. 1986). So, it was used as a rock brittleness concept in this article. The value of the B1brittleness concept is equal to the tangent of ß angle in the following graph. It was seen that more meaningful relationships could be obtained with the B2 brittleness, the under ?Area?(= 1/2(scxsT) = B2) under the curve, instead of tangent ß, (=B1), of the curve.

Jan 1, 2003